Chevrolet 2004 Corvette Owner's Manual page 110

Notice: If you lower the convertible top into the
storage compartment and the rear edge of the top is
not in the full-down position, you could damage
the top. Always verify that the rear edge of the
convertible top is in the full-down position before
lowering the top into the storage compartment.
6. Push forward on the front edge (A) of the
convertible top to allow the rear edge (B) of the
convertible top to be moved to its full-down position.
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7. Then move the top rearward to its fully-stored
position.
8. After the top is stored, apply one even push on the
center of the front edge (A) of the convertible top to
assure that the top is fully retracted.
9. Close the storage compartment lid (C) by closing
with a swift, firm motion.